jmc

Since $\frac{1}{7}$ repeats every 6 digits, so does $3\cdot \frac{1}{7}=\frac{3}{7}$. The 9th digit is therefore the same as the third digit. If we multiply $\frac{1}{7}$ by 3, we get $.4285\dots$, which has a third digit of $\boxed{8}$.